President Obama is expected to announce on Wednesday that the U.S. will take major steps toward normalizing diplomatic relations with Cuba, which have been in a deep freeze since the 1960s. Though these measures will stop short of lifting the embargo—which would require an act of Congress—the move still trails well behind American popular opinion. Even though Fidel Castro has been a national bogeyman for decades, there's less and less appetite in the U.S. for a policy of harsh isolation, even among Cuban Americans, a group that has historically favored strict measures to squeeze the Castro regime.

That isn't to say that Americans have come to look fondly on the Castro brothers. Views of Cuba are still unfavorable by a significant margin—nearly 20 percent—but they've been steadily inching upward since the late 1990s:

What is Your Opinion of Cuba?

Gallup

Yet in every Gallup poll since 1999, a majority of Americans have wanted to normalize relations with Cuba, with the number varying between 55 and 71 percent in favor. And bare majorities—or in one 2000 poll, a plurality—have also supported ending the U.S. embargo against the country.

The greatest bastion of support for the policy of isolation has historically been the Cuban-American community in Florida—people who have fled the Castro regime and their families. As refugees from a communist regime, they've also tended to be far more conservative than other Latinos in the U.S. More recently, however, even Cuban Americans have concluded that the embargo isn't working. (There are also signs that they're moving toward the political center: Obama won the vote bloc in 2012 after losing it in 2008.)

A Florida International University poll in June found that 68 percent of Cuban Americans favor normalized diplomatic relations; 69 percent want travel restrictions to Cuba to end; and 52 percent want the embargo lifted. "We are witnessing a clear demographic shift with younger and more recently arrived Cubans favoring a change in policy toward the island,” said Guillermo J. Grenier, who ran the poll.

The same poll found Cuban-American support for greater engagement even higher—79 percent in Florida and 73 percent nationwide, though with high margins of error because of small samples.

The gradual shift hasn't completely been absorbed by the political class. Democratic candidate Charlie Crist tried to make the embargo an issue in the 2014 gubernatorial race. (He succeeded, but lost the race anyway.) Republican Senator Marco Rubio of Florida, whose parents were born in Cuba and moved to the United States, has opposed looser travel restrictions. Senator Ted Cruz, another Republican whose father was born in Cuba, also opposes lifting the embargo.

Earlier this month, Jeb Bush, the Republican former Florida governor who on Tuesday announced that he's "actively exploring" a presidential bid, said, "I would argue that, instead of lifting the embargo, we should consider strengthening it." As proof that the embargo's backers aren't ready to surrender, the Miami Heraldreported that "the crowd of donors, the backbone of Cuba’s exiled elite, applauded loudly" when Bush made that proposal. But their view looks more beleaguered than ever today.

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David A. Graham is a staff writer at The Atlantic, where he covers U.S. politics and global news.